Summary: PHYSICAL REVIEW B 84, 245409 (2011)
Thermal oscillations of structurally distinct single-walled carbon nanotubes
Polina Pine*
Russel Berrie Nanotechnology Institute, Technion, Haifa 32000, Israel
Yuval E. Yaish
Department of Electrical Engineering, Technion, Haifa 32000, Israel
Joan Adler
Department of Physics, Technion, Haifa 32000, Israel
(Received 5 September 2011; published 9 December 2011)
Zigzag, armchair, and different types of chiral single-walled carbon nanotubes (SWCNTs) have distinct
structures, due to different wrapping vectors of the underlying graphene sheets. The electronic properties depend
on their structure, but this is less clear with regard to their mechanical properties. We modeled the first four flexural
thermal vibrational modes of all three types with clamped ends, as a function of length. We applied a carefully
equilibrated molecular dynamics procedure that was previously validated by comparison with the Timoshenko
beam model in suitable limits. This analytic model allows for both rotary inertia and shearing deformation, but
it cannot differentiate among the three atomistic structures. Comparison between the vibrational behavior of the
three types of nanotubes clearly shows that the SWCNT structure does not affect the vibrational frequencies
under clamped conditions.
DOI: 10.1103/PhysRevB.84.245409 PACS number(s): 62.25.-g
I. INTRODUCTION